K-theory for C*-algebras, and beyond
Serge Richard (firstname.lastname@example.org), Rm. 247 in Sci. Bldg. A
Schedule : Wednesday 8.45 - 10.15
Class dates :
April 22, 29
May 6, 13, 20, 27
June 3, 10, 17, 24
July 1, 8, 15, 22
Weekly summaries :
Student reports :
Solution to Exercise 1.1.6, by Ikuya Ozeki
Solution to Exercise 1.1.6, by Yoshiteru Murai
Solution to Exercise 2.1.6, by Ikuya Ozeki
Solution to Exercises 2.1.10, 2.2.2, 2.2.3 , by Ikuya Ozeki
Solution to Exercise 2.2.2, by Kazumasa Narita
Solution to Exercise 3.1.4, by Kazumasa Narita
Solution to Exercise 3.1.5, by Shinya Kato
Proof of Proposition 3.2.5, by Shinya Kato
Solution to Exercise 3.3.3, by Naohiro Tsuzu
Solution to Exercise 3.4.4, by Shinya Kato
About GNS construction, by Ikuya Ozeki
About unitization of C*-algebras, by Yoshihiko Terasawa
Extension 6.3.4 on Fredholm operators and the index map, by Naohiro Tsuzu
Introduction to topological K-theory, by Xuanrui Qi
References : (electronic version available upon request)
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[Con86] A. Connes, Cyclic cohomology and the transverse fundamental class of a foliation,
in Geometric methods in operator algebras (Kyoto, 1983), 52--144, Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech., Harlow, 1986.
[Con94] A. Connes, Non-commutative geometry, Academic Press, Inc., San Diego, CA, 1994.
[CMR07] J. Cuntz, R. Meyer, J. Rosenberg, Topological and bivariant K-theory, Oberwolfach Seminars, 36. Birkhauser Verlag, Basel, 2007.
[GI03] V. Georgescu, A. Iftimovici, C*-algebras of quantum Hamiltonians, in Operator Algebras and Mathematical Physics,
Conference Proceedings: Constanta (Romania) July 2001, 123-167, Theta Foundation, 2003.
[GVF01] J. Gracia-Bondia, J Varilly, H. Figueroa, Elements of noncommutative geometry,
Birkhauser Advanced Texts, Birkhauser Boston, Inc., Boston, MA, 2001.
[Kha13] M. Khalkhali, Basic noncommutative geometry, EMS Series of Lectures in Mathematics. European Mathematical Society (EMS), Zürich, 2013.
[KS04] J. Kellendonk, H. Schutz-Baldes, Boundary maps for C*-crossed products with R with an application to the quantum Hall effect,
Comm. Math. Phys. 249 no. 3 (2004), 611-637.
[MN08] H. Moriyoshi, T. Natsume, Operator algebras and geometry
Translations of Mathematical Monographs 237, American Mathematical Society, Providence, RI, 2008.
[Mur90] G.J. Murphy, C*-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990.
[Ped89] G. Pedersen, Analysis now, Graduate Texts in Mathematics, 118, Springer-Verlag, New York, 1989.
[Ric15] S. Richard, Levinson's theorem: an index theorem in scattering theory,
Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014,
Operator Theory Advances and Application, Birkhauser.
[RLL00] M. Roerdam, F. Larsen, N. Laustsen, An introduction to K-theory for C*-algebras,
London Mathematical Society Student Texts 49, Cambridge University Press, Cambridge, 2000.
[Yos65] K. Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften 123,
Academic Press, Inc., New York; Springer-Verlag, Berlin 1965.
[W-O93] N.E. Wegge-Olsen, K-theory and C*-algebras, a friendly approach, Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993.
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